基于数据的插值方法，实现对噪声线性系统的轨迹一致性分析与预测。
Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems
- 利用测量数据和先验边界约束，纯数据驱动地刻画所有可能轨迹。
- 可实现数据一致性验证、推断与一步预测，支持安全性和成本优化。
- 适合关注数据驱动控制与系统安全性的研究者。
我们为具有未知系统矩阵（有界范数，意味着有界增长或能量不增）和有界过程噪声能量的噪声线性系统，构建了一个基于插值的框架。该方法以纯数据驱动的方式，表征所有与测量数据及先验边界一致的轨迹。这一表征可用于数据一致性验证、推断与一步前预测，进而支持安全验证与成本最小化。本工作为在数据驱动控制中应用插值条件提供了初步思路，系统性地刻画了给定类动态系统下的一致轨迹，并使其可用于控制设计。
原文摘要 · Abstract (English)
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these prior bounds in a purely data-driven manner. This characterization enables data-consistency verification, inference, and one-step ahead prediction, which can be leveraged for safety verification and cost minimization. Ultimately, this work represents a preliminary step toward exploiting interpolation conditions in data-driven control, offering a systematic way to characterize trajectories consistent with a dynamical system within a given class and enabling their use in control design.
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